An Operating Agreement is the name we give a legal contract for a limited liability company. That contract covers all of the details about your LLC, including who the owners are, what percentage of the LLC they each own, how the LLC will be managed on a day-to-day basis, and how new Members will be added and current Members allowed to leave. These details are very important, even if you are the only owner of your Virginia LLC.
For example, how will you prove that you own your LLC so you can open a bank account? Your name as owner is not in the Articles of Organization filed with the State Corporation Commission. And how will you show that you respected the separate legal nature of the LLC if you get into trouble and a creditor is trying to pierce through the veil of limited liability protection? And will the default laws of Virginia for LLC's be sufficient for how you want to make decisions for your LLC? Without an Operating Agreement, the Virginia Limited Liability Company Act will control the things that happen to your LLC.
So yes, it's important (and useful) to have an Operating Agreement even if you're the only owner. It can be short and simple and doesn't need to include confusing legalese.